Here's the announcement of their marriage in the paper:

http://news.google.com/newspapers?id=JhcxAAAAIBAJ&sjid=QuEFAAAAIBAJ&pg=4232,5936277&dq=lucille+ball+desi+arnaz&hl=en

Oops! In 1944, it seemed to be all over:

http://news.google.com/newspapers?id=GCYiAAAAIBAJ&sjid=-qMFAAAAIBAJ&pg=4560,5396137&dq=lucille+ball+desi+arnaz&hl=en

http://news.google.com/newspapers?id=LDEbAAAAIBAJ&sjid=pkwEAAAAIBAJ&pg=3022,1356695&dq=lucille+ball+desi+arnaz&hl=en

http://news.google.com/newspapers?id=MPAZAAAAIBAJ&sjid=GSMEAAAAIBAJ&pg=2848,5088621&dq=lucille+ball+desi+arnaz&hl=en

Oh that divorce thing? Never mind . . .

http://news.google.com/newspapers?id=DzIdAAAAIBAJ&sjid=GiMEAAAAIBAJ&pg=2569,1626018&dq=lucille+ball+desi+arnaz&hl=en

http://pqasb.pqarchiver.com/courant/access/872437182.html?dids=872437182:872437182&FMT=CITE&FMTS=CITE:AI&type=historic&date=Nov+29,+1944&author=&pub=Hartford+Courant&desc=Luville+Ball+Decides+To+Call+Off+Divorce&pqatl=google